A214444 Arithmetic mean of next a(n) successive squares is prime.

7, 5, 7, 5, 7, 5, 151, 29, 31, 5, 7, 101, 35, 25, 7, 5, 7, 5, 7, 5, 35, 53, 7, 25, 35, 25, 43, 5, 35, 65, 7, 65, 91, 17, 7, 65, 83, 13, 59, 173, 7, 25, 11, 13, 7, 17, 7, 25, 11, 17, 7, 65, 43, 61, 35, 17, 79, 53, 23, 29, 11, 29, 35, 101, 7, 17, 11, 29, 35, 5, 35, 25, 35

Offset

1,1

Comments

Corresponding primes (and arithmetic means):

13, 83, 229, 443, 733, 1091, 14221, 40471, 53441, 62003, 65029, 96331, 142231, 165701, 178933, 184043, 189229, 194483, 199813, 205211, 223831, 267523, 299213, 317021, 351751, 388181, 431803, 463763, 491503, 564353, 619373

Conjecture: for some k and x, a(n)=A214451(n+x) for n>k.

Links

Table of n, a(n) for n=1..73.

Example

(0+1+4+9+16+25+36)/7 = 13, so a(1)=7. The next set of successive squares with prime arithmetic mean: (7^2 + 8^2 + 9^2 +100 + 11^2)/5 = 83, so a(2)=5.

Crossrefs

Cf. A000040, A000290, A214442, A214451.

Sequence in context: A178988 A163505 A021136 * A194657 A230163 A143297

Adjacent sequences: A214441 A214442 A214443 * A214445 A214446 A214447

Keyword

nonn

Author

Alex Ratushnyak, Jul 18 2012

Status

approved